Conflict is a critical element in the narrative, inciting dramatic tension. This paper introduces CNGCI (Conflict-driven Narrative Generation through Commonsense Inference), a neuro-symbolic framework designed to generate coherent stories embedded with conflict using commonsense inference. Our framework defines narrative conflict by leveraging the concept of a soft causal threat, where conflict serves as an obstacle that reduces the likelihood of achieving the protagonist's goal by weakening the causal link between context and goal through defeasible inference. Comparative studies against multiple story generation baselines utilizing commonsense reasoning show that our framework outperforms the baselines in creating narratives that distinctly embody conflict while maintaining coherency.